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Chapter ONE
The Where, Why, and How
of Data Collection
1.1
1.2
1.3
1.4
What is Business Statistics?
Tools for Collecting Data
Populations, Samples, and Sampling Techniques
Data Types and Data Measurement Levels
CHAPTER OUTCOMES
After studying the material in Chapter 1, you should:
1.
2.
3.
4.
Know the key data collection methods.
Know the difference between a population and a sample.
Understand the similarities and differences between different sampling methods.
Understand how to categorize data by type and level of measurement.
PREPARING FOR CHAPTER ONE
•
Locate a recent copy of a business periodical, such as Fortune or Business Week,
and take note of the graphs, charts, and tables that are used in the articles and
advertisements.
•
Recall any recent experiences you have had in which you were asked to complete
a written survey or respond to a telephone survey.
•
Make sure that you have access to Excel or Minitab software. Open either Excel or
Minitab and familiarize yourself with the software.
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WHY YOU NEED
TO
KNOW
Although you may not realize it yet, by taking this business statistics course, you will be learning about some
of the most useful business tools available for decision
makers. In today’s workplace, you can have an immediate
competitive edge over other new employees, and even
those with more experience, by applying statistical analysis skills to real-world decision-making problems. The
purpose of this text is to assist in your learning process and
to complement your instructor’s efforts in conveying how
to apply a variety of important statistical tools. Each chapter introduces one or more statistical tools and techniques
that regardless of your major will be useful in your career.
Wal-Mart, the world’s largest retail chain, collects and
manages massive amounts of data related to the operation
of its stores throughout the world. Its highly sophisticated
database systems contain sales data, detailed customer
data, employee satisfaction data, and much more. General
Motors maintains databases with information on production, quality, customer satisfaction, safety records, and
much more. Governmental agencies amass extensive data
on such things as unemployment, interest rates, incomes,
and education. However, access to data is not limited to
large companies. The relatively low cost of computer hard
drives with 100 gigabyte or larger capacities makes it possible for small firms, and even individuals, to store vast
amounts of data on desktop computers. But without some
way to transform the data into useful information, the data
any of these companies has gathered are of little value.
Transforming data into information is where business
statistics comes in—the statistical tools introduced in this
text are those that are used to help transform data into
information. This text focuses on the practical application
of statistics; we do not develop the theory you would find
in a mathematical statistics course. Will you need to use
math in this course? The answer is yes, but mainly the
concepts covered in your college algebra course.
Statistics does have its own terminology. You will
need to learn various terms that have special statistical
meaning. You will also learn certain do’s and don’ts related
to statistics. But most importantly you will learn specific
methods to effectively convert data into information. Don’t
try to memorize the concepts; rather, go to the next level of
learning called understanding. Once you understand the
underlying concepts, you will be able to think statistically.
Because data are the starting point for any statistical analysis, Chapter 1 is devoted to discussing various
aspects of data, from how to collect data to the different
types of data that you will be analyzing. You need to
gain an understanding of the where, why, and how of data
and data collection because the remaining chapters deal
with the techniques for transforming data into useful
information.
1.1 What is Business Statistics?
Business Statistics
A collection of tools and
techniques that are used to
convert data into meaningful
information in a business
environment.
Every day, your local newspaper contains stories that report descriptors such as stock
prices, crime rates, and government agency budgets. Such descriptors can be found in
many places. However, they are just a small part of the discipline called business statistics
which provides a wide variety of methods to assist in data analysis and decision making.
Business is one important area of application for these methods.
Descriptive Statistics
The tools and techniques that comprise business statistics include those specially designed
to describe data, such as charts, graphs, and numerical measures. Also included are inferential tools that help decision makers draw inferences from a set of data. Inferential tools
include estimation and hypothesis testing. A brief discussion of these tools and techniques
follows. The examples illustrate data that have been entered into the Microsoft Excel and
Minitab software packages.
BAKER CITY HOSPITAL Because health care companies in the United States are facing
increased competition, hospital administrators must become more efficient in managing
operations. This demand means they must better understand their customers.
The financial vice president for Baker City Hospital recently collected data for 138
patients. The VP has entered these data into an Excel spreadsheet called Baker, as illustrated
in Figure 1.1. Each column in the figure corresponds to a different factor for which data were
collected. Each row corresponds to a different patient. Many statistical tools might help the
VP describe these patients’ data, including charts, graphs, and numerical measures.
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FIGURE 1.1
Excel 2007 Spreadsheet
of Baker City Hospital
Patient Data
Excel 2007 Instructions:
1. Open file: Baker.xls.
Charts and Graphs Although we develop an extensive variety of methods to describe
data using graphs and charts in Chapter 2, a few examples are offered here to give you an
idea of what is possible. Figure 1.2 shows a graph called a histogram. This graph gives us
some insight into how long patients stay at the Baker City Hospital by visually showing
how many patients appear in each length-of-stay category. It displays the shape and spread
of the patient length-of-stay distribution. The bar chart shown in Figure 1.3 breaks down
the patient data, showing the percentage of male and female patients. We can tell, looking
at this chart, that the mix of patients has a higher percentage of females.
Chapter 2 will discuss in detail the conditions under which either a histogram or a bar
chart should be used, but we can point out now two basic differences between these two
important graphical tools. First, a bar chart is used to display data that have been categorized
(for example, males and females in Figure 1.3.) A histogram is used to display data over a
range of values for the factor being considered (for example, days in the hospital between 0
and 18 in Figure 1.2). A second difference is that a histogram should have no gaps between
the bars, but we typically do insert gaps between the bars on a bar chart. These differences
will be emphasized again in Chapter 2. Bar charts and histograms are only two of the graphical techniques that the Baker City Hospital VP might use to help describe her patient
population. In Chapter 2 you will learn more about these and other techniques.
FIGURE 1.2
BAKER CITY HOSPITAL—LENGTH OF STAY DISTRIBUTION
Histogram
70
Number of Patients
60
50
40
30
20
10
0
0<2
2<4
4<6
6<8
8 < 10 10 < 12 12 < 14 14 < 16 16 < 18
Days in the Hospital
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FIGURE 1.3
PATIENTS BY GENDER
Bar Chart of Baker City
Hospital
55.80%
Gender
Females
44.20%
Males
0%
10%
20%
30%
Percentage
40%
50%
60%
CROWN INVESTMENTS During the 1990s and early 2000s, many major changes occurred in
the financial services industry. Numerous banks merged. Money flowed into the stock market
at rates far surpassing anything the U.S. economy had previously witnessed. The international
financial world fluctuated greatly. All these developments have spurred the need for more
financial analysts who can critically evaluate financial data and explain them to customers.
At Crown Investments, a senior analyst is preparing to present data to upper
management on the 100 fastest-growing companies on the Hong Kong Stock Exchange.
Figure 1.4 shows a Minitab worksheet containing a subset of the data. The columns correspond to the different items of interest (growth percentage, sales, and so on). The data for
each company are in a single row. The data file is called Fast100.
In addition to preparing appropriate graphs, the analyst will compute important
numerical measures. One of the most basic and most useful measures in business statistics
is one with which you are already familiar: the arithmetic mean or average.
Average
The sum of all the values divided by the number of values. In equation form:
N
Average ∑ xi
i =1
N
Sum of All Data Values
Numbeer of Data Values
where:
N Number of data values
xi ith data value
FIGURE 1.4
Crown Investment
Example—Minitab
Worksheet
(1.1)
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FIGURE 1.5
The Role of Business
Statistics
Data
Statistical Tools
Descriptive
Inferential
Probability
Information
The analyst may be interested in the average profit (that is, the average of the
column labeled “Profits”) for the 100 companies. The total profit for the 100 companies
is $3,193.60, but profits are given in millions of dollars, so the total profit amount is
actually $3,193,600,000. The average is found by dividing this total by the number of
companies:
Average $3, 193, 600, 000
$31, 936, 000, or $31.936 million dollars
100
As we will discuss in greater depth in Chapter 3, the average or mean is a measure of
the center of the data. In this case, the analyst may use the average profit as an indicator—
firms with above-average profits are rated higher than firms with below-average profits.
The graphical and numerical measures illustrated here are only some of the many
descriptive tools that will be introduced in Chapters 2 and 3. The key to remember is that
the purpose of the descriptive tools is to describe data. Your task will be to select the tool
or tools that best accomplish this. As Figure 1.5 reminds you, the role of statistics is to convert data into meaningful information.
Inferential Tools
Statistical Inference Tools
Tools that allow a decision maker
to reach a conclusion about a
set of data based on a subset of
that data.
How do television networks determine which programs people prefer to watch? How does
the network that carries the Super Bowl know how many people were watching the game?
Advertisers pay for TV ads based on the audience level, so these numbers are important;
millions of dollars are at stake. Clearly, the networks don’t check with everyone in the
country. Instead, they use statistical inference tools to come up with the information.
There are two primary categories of statistical inference tools: estimation and hypothesis testing. These tools are closely related but serve very different purposes.
Estimation In situations in which we would like to know about all the data in a large data
set but it is impractical to work with all the data, decision makers can use techniques to
estimate what the larger data set looks like. The estimates are formed by looking closely at
a subset of the larger data set.
TV RATINGS The television networks cannot know for sure how many people watched
last year’s Super Bowl. They cannot possibly ask everyone what he or she saw that day on
television. Instead, the networks rely on organizations that conduct surveys to supply program ratings. For example, the Nielsen Company asks people from only a small number of
homes across the country what shows they watched, and then it uses the data from the
survey to estimate the number of viewers per show for the entire population.
Advertisers and television networks enter into contracts in which price per ad is
based on a certain minimum viewership. If the Nielsen ratings estimate an audience
smaller than this minimum, then a network must refund some money to its advertisers. You
can go to the Web site www.nielsenmedia.com/whatratingsmean to learn more about
TV ratings.
In Chapter 8 we will discuss the estimating techniques that companies such as
Nielsen use.
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Hypothesis Testing Television advertising is full of product claims. For example, we
might hear that “Goodyear tires will last at least 60,000 miles” or that “More doctors
recommend Bayer Aspirin than any other brand.” Other claims might include statements
like “General Electric lightbulbs last longer than any other brand” or “Customers prefer
“McDonald’s over Burger King.” Are these just idle boasts, or are they based on actual
data? Probably some of both! However, consumer research organizations such as
Consumer Reports regularly test these types of claims. For example, in the hamburger
case, Consumer Reports might select a sample of customers who would be asked to blind
taste test Burger King’s and McDonald’s hamburgers, under the hypothesis that there is no
difference in customer preferences between the two restaurants. If the sample data show a
substantial difference in preferences, then the hypothesis of no difference would be
rejected. If only a slight difference in preferences were detected, then Consumer Reports
writers could not reject the hypothesis. Chapters 9 and 10 introduce basic hypothesistesting techniques that are used to test claims about products and services using information taken from samples.
1-1: Exercises
Skill Development
1-1. Consider the following situation and determine
whether the statistical application is primarily
descriptive or inferential.
“The owner of the Holden Pet Store has collected
data for 10 years on the number of each type of
pet that have been sold at his establishment. He is
interested in making a presentation that will illustrate these data effectively.”
1-2. The following graph appeared in a company annual
report. Indicate whether this graph is a bar chart or
a histogram and explain your reasoning.
1-6. Define what is meant by hypothesis testing.
Provide an example in which you personally have
tested a hypothesis (even if you didn’t use formal
statistical techniques to do so.)
1-7. It is important to know when to employ estimation
and when to employ hypothesis testing. Explain
under what circumstances you would use hypothesis testing as opposed to an estimation procedure.
1-8. Discuss any advantages a single measure, such as
an average, has over a table showing a whole set
of data.
1-9. Discuss any advantages a graph showing a whole
set of data has over a single measure, such as an
average.
FOOD STORE SALES
$45,000
Business Applications
1-10. The manager of human resources for the eastern
region for the office-supply company Staples has
collected the following data showing how many
employees there were in each of five categories for
the number of days missed due to illness or injury
during the past year.
$40,000
$35,000
Monthly Sales
$30,000
$25,000
$20,000
$15,000
Missed Days 0–2 days 3–5 days 6–8 days 8–10 days
$10,000
Employees
159
67
32
10
$5,000
$0
Fruit &
Vegetables
Meat and Canned Goods Cereal and
Department Dry Goods
Poultry
Other
1-3. What are the important differences between a bar
chart and a histogram?
1-4. Provide an example of how hypothesis testing can
be used to evaluate a product claim.
1-5. In what situations might a decision maker need to
use statistical inference tools?
Construct the appropriate chart for these data. Be
sure to use labels and add a title to your chart.
1-11. Describe how statistics it could be used by a business to determine if the light bulbs it produces last
longer than the competitor’s brand.
1-12. Suppose The New York Times would like to determine the average age and income of its subscribers.
How could statistics be of use in determining these
values?
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1-13. Locate a business periodical such as Fortune or
Forbes or a business newspaper such as The Wall
Street Journal. Find three examples of the use of a
graph to display data. For each graph.
a. Give the name, date, and page number of the
periodical in which the graph appeared.
b. Describe the main point made by the graph.
c. Analyze the effectiveness of the graphs.
1-14. Considering the types of jobs you might have after
graduating in your own major, discuss one or more
situations where statistical analyses would be used.
Base your answer on research (Internet, business
periodicals, personal interviews, etc.). Indicate
whether the situations you are describing involve
descriptive statistics or inferential statistics or a
combination of both.
1-15. A group of executives at a local company is considering introducing a new product into a market area.
It is important to know the age characteristics of
the people in the market area.
a. If the executives wish to calculate a number that
would characterize the “center” of the age data,
CHAPTER OUTCOME #1
7
what statistical technique would you suggest?
Explain your answer.
b. The executives need to know the percentage
of people in the market area that are senior
citizens. Name the basic category of statistical
tools they would use to determine this
information.
c. Describe a hypothesis which the executives
might wish to test concerning the percentage of
senior citizens in the market area.
1-16. Locate an example from a business periodical
or newspaper in which estimation has been used.
a. What specifically was estimated?
b. What conclusion was reached using the
estimation?
c. Describe how the data were extracted and how
they were used to produce the estimation.
d. Keeping in mind the goal of the estimation, discuss whether you believe that the estimation was
successful and why.
e. Describe what inferences were drawn as a result
of the estimation.
1.2 Tools for Collecting Data
We have defined business statistics as a set of tools that are used to transform data into
information. Before you learn how to use statistical tools, it is important that you become
familiar with different types of data collection methods.
Data Collection Methods
There are many methods and tools available for collecting data. The following are considered some of the most useful and frequently used data collection methods:
experiments
telephone surveys
written questionnaires and surveys
direct observation and personal interviews
Experiments
FOOD PROCESSING A company often must conduct a specific experiment or set of
experiments to get the data managers need to make informed decisions. For example, the
J. R. Simplot Company in Idaho is a primary supplier of french fries to companies such as
McDonald’s. At its Caldwell factory, Simplot has a tech center that, among other things,
houses a mini–french fry plant used to conduct experiments on its potato manufacturing
process. McDonald’s has strict standards on the quality of the french fries it buys.
One important attribute is the color of the fries after cooking. They should be uniformly
“golden brown”—uniformly not too light or too dark.
French fries are made from potatoes that are peeled, sliced into strips, blanched, partially cooked, and then freeze-dried—not a simple process. Because potatoes differ in
many ways (such as sugar content and moisture), blanching time, cooking temperature,
and other factors vary from batch to batch.
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FIGURE 1.6
Data Layout for the
French Fry Experiment
Experiment
Any process that generates data
as its outcome.
Experimental Design
A plan for performing an
experiment in which the variable
of interest is defined. One or
more factors are identified to
be manipulated, changed, or
observed so that the impact
(or influence) on the variable
of interest can be measured
or observed.
Closed-end Questions
Questions that require the
respondent to select from a short
list of defined choices.
Demographic Questions
Questions relating to the
respondents’ characteristics,
backgrounds, and attributes.
Blanch Time
Blanch Temperature
10 minutes
100
110
120
15 minutes
100
110
120
20 minutes
100
110
120
25 minutes
100
110
120
1
Potato Category
2
3
4
Simplot tech-center employees start their experiments by grouping the raw potatoes into
batches with similar characteristics. They run some of the potatoes through the line with
blanch time and temperature settings set at specific levels defined by an experimental design.
After measuring one or more output variables for that run, they change the settings and run
another batch, again measuring the output variables.
Figure 1.6 shows a typical data collection form. The output variable (for example,
percentage of fries without dark spots) for each combination of potato category, blanch
time, and temperature is recorded in the appropriate cell in the table. Chapter 12 introduces
the fundamental concepts related to experimental design and analysis.
Telephone Surveys
PUBLIC ISSUES One common method of obtaining data about people and their opinions is
the telephone survey. Chances are that you have been on the receiving end of one. “Hello. My
name is Mary Jane and I represent the XYZ organization. I am conducting a survey on. . . .”
Political groups use telephone surveys to poll people about candidates and issues.
Telephone surveys are a relatively inexpensive and efficient data collection tool.
Of course, some people will refuse to respond to a survey, others are not home when the
calls come, and some people do not have phones, only have a cell phone, or cannot be
reached by phone for one reason or another.
Figure 1.7 shows the major steps in conducting a telephone survey. This example survey was run by a Seattle television station to determine public support for using tax dollars
to build a new football stadium for the NFL Seattle Seahawks. The survey was aimed at
property-tax payers only.
Because most people will not stay on the line very long, the phone survey must be short—
usually 1 to 3 minutes. The questions are generally what are called closed-end questions. For
example, a closed-end question might be, “To which political party do you belong?
Republican? Democrat? Or other?”
The survey instrument should have a short statement at the beginning explaining the
purpose of the survey and reassuring the respondent that his or her responses will remain
confidential. The initial section of the survey should contain questions relating to the central issue of the survey. The last part of the survey should contain demographic questions
(such as gender, income level, and education level) that will allow you to break down the
responses and look deeper into the survey results.
A survey budget must be considered. For example, if you have $3,000 to spend on
calls and each call costs $10 to make, you obviously are limited to making 300 calls.
However, keep in mind that 300 calls may not result in 300 usable responses.
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FIGURE 1.7
Major Steps for a
Telephone Survey
Define the
Issue
Define the
Population
of Interest
Develop
Survey
Questions
Pretest
the
Survey
Determine
Sample Size and
Sampling Method
Select Sample
and
Make Calls
Do taxpayers favor a special bond to build a new football stadium
for the Seahawks? If so, should the Seahawk owners share the cost?
Population is all residential property-tax payers in King County,
Washington. The survey will be conducted among this group only.
Limit the number of questions to keep survey short.
Ask important questions first. Provide specific response options
when possible.
Establish eligibility. “Do you own a residence in King County?”
Add demographic questions at the end: age, income, etc.
Introduction should explain purpose of survey and who is
conducting it—stress that answers are anonymous.
Try the survey out on a small group from the population. Check for
length, clarity, and ease of conducting. Have we forgotten anything?
Make changes if needed.
Sample size is dependent on how confident we want to be of our
results, how precise we want the results to be, and how much
opinions differ among the population members. Chapter 7 will
show how sample sizes are computed. Various sampling methods
are available. These are reviewed later in Chapter 1.
Get phone numbers from a computer-generated or “current” list.
Develop “callback” rule for no answers. Callers should be trained to
ask questions fairly. Do not lead the respondent. Record responses
on data sheet.
The phone survey should be conducted in a short time period. Typically, the prime
calling time for a voter survey is between 7:00 P.M. and 9:00 P.M. However, some people are
not home in the evening and will be excluded from the survey unless there is a plan for
conducting callbacks.
Written Questionnaires and Surveys The most frequently used method to collect
Open-end Questions
Questions that allow respondents
the freedom to respond with any
value, words, or statements of
their own choosing.
opinions and factual data from people is a written questionnaire. In some instances, the
questionnaires are mailed to the respondent. In others, they are administered directly to the
potential respondents. Written questionnaires are generally the least expensive means of
collecting survey data. If they are mailed, the major costs include postage to and from the
respondents, questionnaire development and printing costs, and data analysis.
Figure 1.8 shows the major steps in conducting a written survey. Note how written
surveys are similar to telephone surveys; however, written surveys can be slightly more
involved and, therefore, take more time to complete than those used for a telephone survey.
However, you must be careful to construct a questionnaire that can be easily completed
without requiring too much time.
A written survey can contain both closed-end and open-end questions.
Open-end questions provide the respondent with greater flexibility in answering a
question; however, the responses can be difficult to analyze. Note that telephone surveys
can use open-end questions, too. However, the caller may have to transcribe a potentially
long response and may misinterpret what is being said.
Written surveys also should be formatted to make it easy for the respondent to provide
accurate and reliable data. This means that proper space must be provided for the
responses and the directions must be clear about how the survey is to be completed.
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FIGURE 1.8
Written Survey Steps
Define the
Issue
Define the
Population
of Interest
Design the
Survey
Instrument
Pretest
the
Survey
Determine
Sample Size and
Sampling Method
Select Sample
and
Send Surveys
Clearly state the purpose of the survey. Define the objectives. What
do you want to learn from the survey? Make sure there is agreement
before you proceed.
Define the overall group of people to be potentially included in the
survey and obtain a list of names and addresses of those individuals
in this group.
Limit the number of questions to keep the survey short.
Ask important questions first. Provide specific response options
when possible.
Add demographic questions at the end: age, income, etc.
Introduction should explain purpose of survey and who is
conducting it—stress that answers are anonymous.
Layout of the survey must be clear and attractive. Provide location
for responses.
Try the survey out on a small group from the population. Check for
length, clarity, and ease of conducting. Have we forgotten anything?
Make changes if needed.
Sample size is dependent on how confident we want to be of our
results, how precise we want the results to be, and how much
opinions differ among the population members. Chapter 7 will
show how sample sizes are computed. Various sampling methods
are available. These are reviewed later in Chapter 1.
Mail survey to a subset of the larger group.
Include a cover letter explaining the purpose of the survey.
Include return envelope for returning the survey.
A written survey needs to be pleasing to the eye. How it looks will affect the response rate,
so it must look professional.
You also must decide whether to manually enter or scan the data gathered from your
written survey. The survey design will be affected by the approach you take. If you are
administering a large number of surveys, scanning is preferred. It cuts down on data entry
errors and speeds up the data gathering process. However, you may be limited in the form
of responses that are possible if you use scanning.
If the survey is administered directly to the desired respondents, you can expect a high
response rate. For example, you probably have been on the receiving end of a written survey
many times in your college career, when you were asked to fill out a course evaluation form
at the end of the term. Most students will complete the form. On the other hand, if a survey is
administered through the mail, you can expect a low response rate—typically 5% to 20%.
Therefore, if you want 200 responses, you should mail out 1,000 to 4,000 questionnaires.
Overall, written surveys can be a low-cost, effective means of collecting data if you
can overcome the problems of low response. Be careful to pretest the survey and spend
extra time on the format and look of the survey instrument.
Developing a good written questionnaire or telephone survey instrument is a major
challenge. Among the potential problems are the following:
Leading Questions
Example: “Do you agree with most other reasonably minded people that the city
should spend more money on neighborhood parks?”
Issue: In this case, the phrase “Do you agree” may suggest that you should
agree. Also, by suggesting that “most reasonably minded people” already
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agree, the respondent might be compelled to agree so that he or she can also
be considered “reasonably minded.”
Improvement: “In your opinion, should the city increase spending on neighborhood parks?”
Example: “To what extent would you support paying a small increase in your
property taxes if it would allow poor and disadvantaged children to have food
and shelter?”
Issue: The question is ripe with emotional feeling and may imply that if you
don’t support additional taxes, you don’t care about poor children.
Improvement: “Should property taxes be increased to provide additional funding for social services?”
Poorly Worded Questions
Example: “How much money do you make at your current job?”
Issue: The responses are likely to be inconsistent. When answering, does the
respondent state the answer as an hourly figure or as a weekly or monthly
total? Also, many people refuse to answer question regarding their income.
Improvement: “Which of the following categories best reflects your monthly
income from your current job?
_______ Under $500
_______ Over $1,000”
_______ $500–$1,000
Example: “After trying the new product, please provide a rating from 1 to 10 to
indicate how you like its taste and freshness.”
Issue: First, is a low number or a high number on the rating scale considered a
positive response? Second, the respondent is being asked to rate two factors,
taste and freshness, in a single rating. What if the product is fresh but does not
taste good?
Improvement: “After trying the new product, please rate its taste on a 1 to 10 scale
with 1 being best. Also rate the product’s freshness using the same 1 to 10 scale.
_______ Taste
_______ Freshness”
Another problem is inappropriate choice of vocabulary. If you don’t match the
terms used to the reading and knowledge level of the respondents, they will struggle
to complete the survey and may simply leave questions blank. The best advice is to
use simple vocabulary and very direct questions.
Example: “Please provide your response to each of the following statements using
the Likert scale provided:
Strongly
Agree
Agree
Neutral
Strongly
Disagree Disagree
The cuisine was above reproach.
1
2
3
4
5
The ambiance was divine.
1
2
3
4
5
The service was impeccable.
1
2
3
4
5
Issue: First, how many respondents will be confused by the term Likert scale?
There is no need to name the scale being used. Second, terms like cuisine,
ambiance, divine, and impeccable might be unfamiliar to some respondents.
Improvement: “Please indicate your degree of agreement or disagreement with
each of the following by circling the appropriate number:
Strongly
Agree
Agree
Neutral
Strongly
Disagree Disagree
The food was excellent.
1
2
3
4
5
The atmosphere was pleasant.
1
2
3
4
5
The service was great.
1
2
3
4
5
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Structured Interview
Interviews in which the questions
are scripted.
Unstructured Interview
Interviews that begin with one or
more broadly stated questions,
with further questions being based
on the responses.
Direct Observation and Personal Interviews Direct observation is another tool that
is often used to collect data. As implied by the name, this technique requires that the
process from which the data are being collected is physically observed and the data
recorded based on what takes place in the process.
Possibly the most basic way to gather data on human behavior is to watch people.
If you are trying to decide whether a new method of displaying your product at the supermarket will be more pleasing to customers, change a few displays and watch customers’
reactions. If, as a member of a state’s transportation department, you want to determine
how well motorists are complying with the state’s seat belt laws, place observers at key
spots throughout the state to monitor people’s seat belt habits. If, as a movie producer, you
want information on whether your new movie will be a success, hold a preview showing
and observe the reactions and comments of the movie patrons as they exit the screening.
The major constraints when collecting observations are the time and money it takes to
carry out the observations. For observations to be effective, trained observers must be used,
which increases the cost. Personal observation is also time-consuming. Finally, personal
perception is subjective. There is no guarantee that different observers will see a situation
in the same way, much less report it the same way.
Personal interviews are often used to gather data from people. Interviews can be either
structured or unstructured, depending on the objectives, and they can utilize either openend or closed-end questions.
Regardless of the tool used for data collection, care must be taken that the data collected are accurate and reliable and that they are the right data for the purpose at hand.
Other Data Collection Methods
Data collection methods that take advantage of new technologies are becoming more
prevalent all the time. For example, many people believe that Wal-Mart is the best company in the world at collecting and using data about the buying habits of its customers.
Most of the data are collected automatically as checkout clerks scan the UPC bar codes on
the products customers purchase. Not only are Wal-Mart’s inventory records automatically
updated, but information about the buying habits of customers is recorded. The data help
managers organize their stores to increase sales. For instance, Wal-Mart apparently
decided to locate beer and disposable diapers close together when it discovered that many
male customers also purchase beer when they are sent to the store for diapers.
Bar code scanning is used in many different data collection applications. In a DRAM
wafer fabrication plant, batches of silicon wafers have bar codes. As the batches travel
through the plant’s workstations, their progress and quality are tracked through the data
that are automatically obtained by scanning.
Every time you use your credit card, data are automatically collected by the retailer
and the bank. Computer information systems are developed to store the data and to provide
decision makers with tools to access the data.
In many instances your data collection method will require you to use physical measurement. For example, the Anderson Window Company has quality analysts physically
measure the width and height of its windows to assure that they meet customer specifications, and a state Department of Weights and Measures will physically test meat and produce scales to determine that customers are being properly charged for their purchases.
Data Collection Issues
There are several data collection issues of which you need to be aware. When you need
data to make a decision, we suggest that you first see if appropriate data have already been
collected, because it is usually faster and less expensive to use existing data than to collect
data yourself. However, before you rely on data that were collected by someone else for
another purpose, you need to check out the source to make sure that the data were collected
and recorded properly.
Such organizations as Value Line and Fortune have built their reputations on providing
quality data. Although data errors are occasionally encountered, they are few and far
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between. You really need to be concerned with data that come from sources with
which you are not familiar. This is an issue for many sources on the World Wide Web. Any
organization, or any individual, can post data to the Web. Just because the data are there
doesn’t mean they are accurate. Be careful.
Interviewer Bias There are other general issues associated with data collection. One of
these is the potential for bias in the data collection. There are many types of bias. For
example, in a personal interview, the interviewer can interject bias (either accidentally or
on purpose) by the way she asks the questions, by the tone of her voice, or by the way she
looks at the subject being interviewed. We recently allowed ourselves to be interviewed at
a trade show. The interviewer began by telling us that he would only get credit for the interview if we answered all of the questions. Next, he asked us to indicate our satisfaction with
a particular display. He wasn’t satisfied with our less-than-enthusiastic rating and kept asking us if we really meant what we said. He even asked us if we would consider upgrading
our rating! How reliable do you think these data will be?
Nonresponse Bias Another source of bias that can be interjected into a survey data col-
lection process is called nonresponse bias. We stated earlier that mail surveys suffer from
a high percentage of unreturned surveys. Phone calls don’t always get through, or people
refuse to answer. Subjects of personal interviews may refuse to be interviewed. There is a
problem with nonresponse. Those who respond may provide data that are quite different
from the data that would be supplied by those who choose not to respond. If you aren’t
careful, the responses may be heavily weighted by people who feel strongly one way or
another on an issue.
Selection Bias Bias can be interjected through the way subjects are selected for data col-
lection. This is referred to as selection bias. A study on the virtues of increasing the student
athletic fee at your university might not be best served by collecting data from students
attending a football game. Sometimes, the problem is more subtle. If we do a telephone
survey during the evening hours, we will miss all of the people who work nights. Do they
share the same views, income, education levels, and so on as people who work days? If
not, the data are biased.
Written and phone surveys and personal interviews can also yield flawed data if the
interviewees lie in response to questions. For example, people commonly give inaccurate
data about such sensitive matters as income. Sometimes, the data errors are not due to lies.
The respondents may not know or have accurate information to provide the correct answer.
Observer Bias Data collection through personal observation is also subject to problems.
People tend to view the same event or item differently. This is referred to as observer bias.
One area in which this can easily occur is in safety check programs in companies. An
important part of behavioral-based safety programs is the safety observation. Trained data
collectors periodically conduct a safety observation on a worker to determine what, if any,
unsafe acts might be taking place. We have seen situations in which two observers will
conduct an observation on the same worker at the same time, yet record different safety
data. This is especially true in areas in which judgment is required on the part of the
observer, such as the distance a worker is from an exposed gear mechanism. People judge
distance differently.
Measurement Error A few years ago we were working with a window manufacturer.
The company was having a quality problem with one of its saws. A study was developed to
measure the width of boards that had been cut by the saw. Two people were trained to use
digital calipers and record the data. This caliper is a U-shaped tool that measures distance
(in inches) to three decimal places. The caliper was placed around the board and squeezed
tightly against the sides. The width was indicated on the display. Each person measured 500
boards during an 8-hour day. When the data were analyzed, it looked like the widths were
coming from two different saws; one set showed considerably wider widths than the other.
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Upon investigation, we learned that the person with the narrower width measurements was
pressing down on the calipers much more firmly. The soft wood reacted to the pressure and
gave narrower readings. Fortunately, we had separated the data from the two data collectors.
Had they been merged, the measurement error might have gone undetected.
Internal Validity
A characteristic of an experiment
in which data are collected in such
a way as to eliminate the effects of
variables within the experimental
environment that are not of
interest to the researcher.
External Validity
A characteristic of an experiment
whose results can be generalized
beyond the test environment so
that the outcomes can be
replicated when the experiment
is repeated.
Internal Validity When data are collected through experimentation, you need to make
sure that proper controls have been put in place. For instance, suppose a drug company
such as Pfizer is conducting tests on a drug that it hopes will reduce cholesterol. One group
of test participants is given the new drug while a second group (a control group) is given a
placebo. Suppose that after several months, the group using the drug did see significant
cholesterol reduction. For the results to have internal validity, the drug company
would have had to make sure the two groups did not have statistically different values
for the many other factors that might affect cholesterol, such as smoking, diet, weight,
gender, race, and exercise habits. Issues of internal validity are generally addressed by
randomly assigning subjects to the test and control groups. However, if the extraneous
factors are not controlled, there could be no assurance that the drug was the factor influencing reduced cholesterol. For data to have internal validity, the extraneous factors must
be controlled.
External Validity Even if experiments are internally valid, you will always need to be concerned that the results can be generalized beyond the test environment. For example, if the
cholesterol drug test had been performed in Europe, would the same basic results occur for
people in North America, South America, or elsewhere? For that matter, the drug company
would also be interested in knowing whether the results could be replicated if other subjects
are used in a similar experiment. If the results of an experiment can be replicated for groups
different than the original population, then there is evidence the results of the experiment
have external validity.
An extensive discussion of how to measure the magnitude of bias and how to reduce
bias and other data collection problems is beyond the scope of this text. However, you
should be aware that data may be biased or otherwise flawed. Always pose questions about
the potential for bias and determine what steps have been taken to reduce its affect.
1-2: Exercises
Skill Development
1-17. What is a leading question? Provide an example.
1-18. Briefly explain what is meant by an experiment and
an experimental design.
1-19. If a bank wishes to determine the level of customer
satisfaction with its services, would it be appropriate to conduct an experiment? Explain.
1-20. What type of bias is most likely to occur when a
personal interview is conducted? Explain.
1-21. For each of the following situations, indicate
what type of data collection method you would
recommend and discuss why you have made that
recommendation:
a. collecting data on the percentage of bike riders
who wear helmets.
b. collecting data on the price of regular unleaded
gasoline at gas stations in your state.
c. collecting data on customer satisfaction with the
service provided by a major U.S. airline.
1-22. Suppose a survey is conducted using a telephone
survey method. The survey is conducted from 9 A.M.
to 11 A.M. on Tuesday. Indicate what potential problems the data collectors might encounter.
1-23. Assume you have received a class assignment to
determine the attitude of students in your school
toward the school’s registration process. What are
the validity issues you should be concerned with?
Business Applications
1-24. Briefly describe how new technologies can assist
businesses in their data collection efforts.
1-25. The U.S. Department of Agriculture (USDA) estimates that the Southern fire ants spread at a rate of
4 to 5 miles a year. What data collection method do
you think was used to collect this data? Explain
your answer.
1-26. Assume you have made an airline reservation using
an online service (like Orbitz or Travelocity). The
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following day you receive an e-mail containing a
questionnaire asking you to rate the quality of the
experience. Discuss both the advantages and disadvantages of using this form of questionnaire delivery.
1-27. Suppose you are asked to survey students at your
university to determine if they are satisfied with the
food service choices on campus. What types of
biases must you guard against in collecting your
data?
1-28. An end-of-aisle display is a common method retail
stores use to promote new products. A regional
manager of a national chain is experimenting with
two new displays of the same product. You have
been hired to determine which is more effective.
Two measures you have decided to take are which
display causes the highest percentage of people to
stop, and for those who stop, which causes people
to view the display the longest. Discuss how you
would gather such data.
1-29. Assume that you work for Gold’s Gym, a large fitness chain. You have been asked to survey the customers of your location to determine whether they
want to convert the racquetball courts to aerobics
CHAPTER OUTCOME #2
Population
The set of all objects or individuals
of interest or the measurements
obtained from all objects or
individuals of interest.
Sample
A subset of the population.
Business
Application
Census
An enumeration of the entire set
of measurements taken from the
whole population.
15
exercise space. The plan calls for a written survey
to be handed out to customers when they arrive at
the fitness center. Your task is to develop a short
questionnaire with at least three “issue” questions
and at least three “demographic” questions. You
also need to provide the finished layout design for
the questionnaire.
1-30. In your capacity as assistant sales manager for a
large office products retailer, you have been
assigned the task of interviewing purchasing managers for medium and large companies in the San
Francisco Bay area. The objective of the interview
is to determine the office products buying plans of
the company in the future year. Develop a personal
interview form that asks both issue-related questions as well as demographic questions.
1-31. According to a national CNN/USA/Gallup survey
of 1,007 adults, conducted August 28–30, 2005,
69% of Americans say they have experienced a
hardship because of rising gasoline prices. How do
you believe the survey was conducted and what
types of bias could occur in the data collection
process?
1.3 Populations, Samples,
and Sampling Techniques
Populations and Samples
Two of the most important terms in statistics are population and sample.
The list of all objects or individuals in the population is referred to as the frame. The
choice of the frame depends on what objects or individuals you wish to study and on the
availability of the list of these objects or individuals. Once the frame is defined, it forms
the list of sampling units. The next example illustrates what we mean.
CPA FIRM We can use a certified public accounting (CPA) firm to illustrate the difference
between a population and a sample. When preparing to audit the financial records of a
business, a CPA firm must determine the number of accounts to examine. Until recently,
good accounting practice dictated that the auditors verify the balance of every account and
each financial transaction. Though this is still done in some audits, the size and complexity
of most businesses have forced accountants to select only some accounts and some transactions to audit.
Suppose one part of the financial audit is to verify the accounts receivable balances.
A population includes measurements made on all the items of interest to the data gatherer.
In our example, the accountant would define the population as all accounts receivable balances on record. The list of these accounts, possibly by account number, forms the frame.
If she examines the entire population, she is taking a census. But suppose there are too
many accounts receivable balances to work through. The CPA would then select a subset
of the accounts, called a sample. The accountant uses the sample results to make inferences about the population. If the sample balances look good, she might conclude that the
population balances also are acceptable. How inferences are drawn will be discussed at
greater length in later chapters.
There are trade-offs between taking a census and taking a sample. Usually the
main trade-off is whether the information gathered in a census is worth the extra cost.
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In organizations in which data are stored on computer files, the additional time and effort
of taking a census may not be substantial. However, if there are many accounts that must
be manually checked, a census may be impractical.
Another consideration is that the measurement error in census data may be greater
than in sample data. A person obtaining data from fewer sources tends to be more complete and thorough in both gathering and tabulating the data. As a result, with a sample
there are likely to be fewer human errors.
Parameters and Statistics Descriptive numerical measures, such as an average or a
proportion, that are computed from an entire population are called parameters.
Corresponding measures for a sample are called statistics. In the previous example,
if the CPA examined every accounts receivable balance, the proportion of correct
balances would be a parameter, because it reflects the value for the population.
However, if she selected a sample of balances from the population, the proportion of
accurate balances in this sample is a statistic. These concepts are more fully discussed
in Chapters 3 and 7.
Statistical Sampling
Techniques
Those sampling methods that use
selection techniques based on
chance selection.
Nonstatistical Sampling
Techniques
Those methods of selecting
samples using convenience,
judgment, or other nonchance
processes.
Business
Application
Convenience Sampling
A sampling technique that selects
the items from the population
based on accessibility and ease of
selection.
Sampling Techniques
Once a manager decides to gather information by sampling, he can use a sampling technique that falls into one of two categories: statistical or nonstatistical.
Both nonstatistical and statistical sampling techniques are commonly used by decision makers. Regardless of which technique is used, the decision maker has the same
objective—to obtain a sample that is a close representative of the population. There are
some advantages to using a statistical sampling technique, as we will discuss at many
places throughout this text. However, in many cases, nonstatistical sampling represents the
only feasible way to sample, as illustrated in the following example.
Nonstatistical Sampling
FORD MOTOR COMPANY In 2002, Ford opened an assembly plant in Bahia, Brazil. Parts
arrive at the plant in large quantities from a variety of suppliers at various locations around
the world. As parts are unloaded, quality analysts select a small sample of parts from the top
of each container in the shipment to verify that the parts meet Ford’s specifications. One or
two parts are selected from each container, and based on the findings in the sample, a decision is made whether to accept the entire shipment. Because of the volume of parts, the
assembly plant uses a nonstatistical sampling method called convenience sampling. In
doing so, the quality analysts are willing to assume that the defective parts are evenly spread
throughout the container. That is, the parts near the top of each container are no more likely
or less likely to meet specifications than parts located anywhere else in the container.
There are other nonstatistical sampling methods, such as judgment sampling and ratio
sampling, which we will not discuss here. Instead, we now turn your attention to the most
frequently used statistical sampling techniques.
Statistical Sampling
Statistical sampling methods (also called probability sampling) allow every item in the
population to have a known or calculable chance of being included in the sample. The fundamental statistical sample is called a simple random sample. Other types of statistical
sampling discussed in this text include stratified random sampling, systematic sampling,
and cluster sampling.
Simple Random Sampling
Business
Application
BAIRD LIFE AND CASUALTY A salesperson at Baird Life and Casualty in Charleston,
West Virginia, wishes to estimate the percentage of people in a local subdivision who
already have life insurance policies. The result would indicate the potential market. The
population of interest consists of all families living in the subdivision.
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CHAPTER OUTCOME #3
17
For this example, we simplify the situation by saying that there are only five families
in the subdivision: James, Sanchez, Lui, White, and Fitzpatrick. We will let N be the
population size and n be the sample size. From the five families (N 5), we select three
(n 3) for the sample. There are 10 possible samples of size 3 that could be selected.
{James, Sanchez, Lui} {James, Sanchez, White} {James, Sanchez, Fitzpatrick}
{James, Lui, White}
{James, Lui, Fitzpatrick} {James, White, Fitzpatrick}
{Sanchez, Lui, White} {Sanchez, Lui, Fitzpatrick} {Sanchez, White, Fitzpatrick}
{Lui, White, Fitzpatrick}
Simple Random Sampling
A method of selecting items
from a population such that
every possible sample of a
specified size has an equal
chance of being selected.
Business
Application
Excel and Minitab Tutorial
Note that no family is selected more than once in a given sample. This method is
called sampling without replacement and is the most commonly used method. If the
families could be selected more than once, the method would be called sampling with
replacement.
Simple random sampling is the method most people think of when they think of
random sampling.
In a correctly performed simple random sample, each of these samples would have an
equal chance of being selected. A simplified way of doing this would be to put each sample of three names on a piece of paper in a bowl and then blindly reach in and select one
piece of paper. This method would be difficult to do if the number of possible samples
were large. For example, if N 50 and a sample of size n 10 is to be selected, there are
more than 10 billion possible samples. Try finding a bowl big enough to hold those!
Simple random samples can be obtained in a variety of ways. We will present several
examples to illustrate how simple random samples are selected in practice.
NORDSTROM’S PAYROLL Suppose the personnel manager at Nordstrom’s Department
Store in Seattle is considering changing the payday from once a month to once every two
weeks. Before making any decisions, he wants to survey a sample of 10 employees from
the store’s 300 employees. He first assigns employees a number (001 to 300). He can then
use the random number function in either Excel or Minitab to determine which employees
to include in the sample. Figure 1.9, shows the results when Excel chooses 10 random
numbers. The first employee sampled is number 115, followed by 31, and so forth. The
important thing to remember is that assigning each employee a number and then randomly
selecting a sample from those numbers gives each possible sample an equal chance of
being selected.
Random Number Table If you don’t have access to computer software such as Excel or
Minitab, the items in the population to be sampled can be determined by using the random
numbers table in Appendix A. Begin by selecting a starting point in the random numbers
table (row and digit). Suppose we use row 5, digit 8 as the starting point. Go down 5 rows
and over 8 digits. Verify that the digit in this location is 1. Ignoring the blanks between
FIGURE 1.9
Excel 2007 Output of
Random Numbers for
Nordstrom’s Example
To convert numbers to integers,
select the data in column A and
on the Home tab in the Number
group, click the Decrease
decimal button several times.
Excel 2007 Instructions:
1. On the Formulas tab, click Data
Analysis.
2. Select Random Number
Generation option.
3. Select Uniform as the
distribution.
4. Define range as between 1 and
300.
5. Indicate where the results are
to go.
6. Click OK.
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columns that are there only to make the table more readable, the first three-digit number
is 149. Employee number 149 is the first one selected in the sample. Each subsequent random number is obtained from the random numbers in the next row down. For instance, the
second number is 127. The procedure continues selecting numbers from top to bottom in
each subsequent column. Numbers exceeding 300 and duplicate numbers are skipped.
When enough numbers are found for the desired sample size, the process is completed.
Employees whose numbers are chosen are then surveyed.
Stratified Random Sampling
Business
Application
Stratified Random Sampling
A statistical sampling method in
which the population is divided
into subgroups called strata so that
each population item belongs to
only one stratum. The objective is
to form strata such that the
population values of interest
within each stratum are as much
alike as possible. Sample items are
selected from each stratum using
the simple random sampling
method.
FEDERAL RESERVE BANK Sometimes, the sample size required to obtain a needed level
of information from a simple random sampling may be greater than our budget permits. At
other times, it may take more time to collect than is available. Stratified random
sampling is an alternative method that has the potential to provide the desired information
with a smaller sample size. The following example illustrates how stratified sampling is
performed.
Each year, the Federal Reserve Board asks its staff to estimate the total cash holdings
of U.S. financial institutions as of July 1. The staff must base its estimate on a sample.
Note that not all financial institutions (banks, credit unions, and the like) are the same size.
A majority are small, some are medium-sized, and only a few are large. However, the few
large institutions have a substantial percentage of the total cash on hand. To make sure that
a simple random sample includes an appropriate number of small, medium, and large institutions, the sample size might have to be quite large.
As an alternative to the simple random sample, the Federal Reserve staff could divide
the institutions into three groups called strata: small, medium, and large. Staff members
could then select a simple random sample of institutions from each stratum and estimate
the total cash on hand for all institutions from this combined sample. Figure 1.10 shows the
stratified random sampling concept. Note that the combined sample size (n1 n2 n3) is
the sum of the simple random samples taken from each stratum.
The key behind stratified sampling is to develop strata for the characteristic of interest
(such as cash on hand), that have items that are quite homogeneous. In this example, the size
of the financial institution may be a good factor to use in stratifying. Here the combined
sample size (n1 n2 n3) will be less than the sample size that would have been required
if no stratification had occurred. Because sample size is directly related to cost (in both time
and money), a stratified sample can be more cost-effective than a simple random sample.
FIGURE 1.10
Stratified Sampling
Example
Population:
Cash Holdings
of All Financial
Institutions in
the United States
Financial Institutions
Stratified Population
Stratum 1
Large Institutions
Select n1
Stratum 2
Medium-Size Institutions
Select n2
Stratum 3
Small Institutions
Select n3
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Multiple layers of stratification can further reduce the overall sample size. For example, the Federal Reserve might break the three strata in Figure 1.10 into substrata based on
type of institution: state bank, interstate bank, credit union, and so on.
Most large-scale market research studies use stratified random sampling. The wellknown political polls, such as the Gallup and Harris polls, use this technique also. For
instance, the Gallup poll typically samples between 1,800 and 2,500 people nationwide to
estimate how more than 60 million people will vote in a presidential election. We encourage you to go to the Web site www.gallup.com/help/FAQs/poll1.asp to read a very good
discussion about how the Gallup polls are conducted. It talks about how samples are
selected and many other interesting issues associated with polling.
Systematic Random Sampling
Business
Application
Systematic Random
Sampling
A statistical sampling technique
that involves selecting every kth
item in the population after a
randomly selected starting point
between 1 and k. The value of k is
determined as the ratio of the
population size over the desired
sample size.
NATIONAL ASSOCIATION OF ACCOUNTANTS A few years ago, the National
Association of Accountants (NAA) considered establishing a code of ethics. To determine
the opinion of its 20,000 members, a questionnaire was sent to a sample of 500 members.
Although simple random sampling could have been used, an alternative method called
systematic random sampling was chosen.
The NAA’s systematic random sampling plan called for it to send the questionnaire to
every 40th member (20,000/500 40) from the list of members. The list was in alphabetical order. It could have begun by using Excel or Minitab to generate a single random number in the range 1 to 40. Suppose this value was 25. The 25th person in the alphabetic list
would be selected. After that, every 40th member would be selected (25, 65, 105, 145, . . . )
until there were 500 NAA members.
Systematic sampling is frequently used in business applications. Use it as an alternative to simple random sampling only when you can assume the population is randomly
ordered with respect to the measurement being addressed in the survey. In this case, peoples’ views on ethics are likely unrelated to the spelling of their last name.
Cluster Sampling
Business
Application
WASHINGTON GROUP INTERNATIONAL When using a telephone survey or a mail questionnaire, the geographical location of the respondents is not a significant data collection
issue. However, in some instances when physical measurement or observation is required
to collect the data, location can be an important issue.
Suppose Washington Group International, a large worldwide construction company,
wants to develop a new corporate bidding strategy. Upper management wants input on possible new strategies from its middle-level managers. Assume that Figure 1.11 illustrates the
current distribution of middle-level managers throughout the world. For example, there are
25 middle-level managers in Algeria, 47 in Illinois, and so forth. Upper management
decides to hold face-to-face personal interviews with a sample of these mid-level managers.
One sampling technique is to select a simple random sample of size n from the population of middle managers. Unfortunately, this technique would likely require that
interviewer(s) go to each state or country in which Washington Group International has
middle-level managers. This would prove to be an expensive and time-consuming process.
A systematic or stratified sampling procedure also would probably require visiting each
location. The geographical spread in this case causes problems.
FIGURE 1.11
Mid-Level Managers by Location for Washington Group International
Algeria
Illinois
Scotland
California
Alaska
New York
Florida
Idaho
Mexico
Australia
25
47
22
105
20
36
52
152
76
37
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Cluster Sampling
A method by which the population
is divided into groups, or clusters,
that are each intended to be minipopulations. A simple random
sample of m clusters is selected.
The items chosen from a cluster
can be selected using any
probability sampling technique.
A sampling technique that overcomes the traveling (time and money) problem is
cluster sampling. Ideally, the clusters would each have the same characteristics as the
population as a whole. In the Washington Group International example, the states or countries where the company has managers would be the clusters.
After the clusters have been defined, a sample of m clusters is selected at random from
the list of possible clusters. The number of clusters to select depends on various factors,
including our survey budget. Suppose WGI selects m 3 clusters randomly as follows:
Scotland
Florida
Illinois
These are the primary clusters. Next, the company can either survey all the managers in
each cluster or select a simple random sample of managers from each cluster, depending
on time and budget considerations.
1-3: Exercises
Skill Development
1-32. A parts file has 18,000 different part items. The file
is ordered by part number from 1 to 18,000. If a
sample of 100 parts is to be selected from the
18,000 parts using systematic random sampling,
within what range of part numbers will the first
part selected come from?
1-33. Indicate which sampling method would most likely
be used in each of the following situations:
a. an interview conducted with mayors of a sample
of cities in Florida
b. a poll of voters regarding a referendum calling
for a national value-added tax
c. a survey of customers entering a shopping mall
in Minneapolis
1-34. Briefly describe the difference between a parameter
and a statistic.
1-35. Describe how systematic random sampling could
be used to select a random sample of 1,000 customers who have a certificate of deposit at a commercial bank. Assume that the bank has 25,000
customers who own a certificate of deposit.
1-36. If a manager surveys a sample of 100 customers to
determine how many miles they live from the store,
is the mean travel distance for this sample considered a parameter or a statistic? Explain.
1-37. Why is convenience sampling considered to be a
nonstatistical sampling method?
1-38. Explain the difference between stratified random
sampling and cluster sampling.
1-39. Explain why a census does not necessarily have to
involve a population of people. Use an example to
illustrate.
1-40. Use Excel or Minitab to generate five random numbers between 1 and 900.
Business Applications
1-41. Give the name of the kind of sampling that was
most likely used in each of the following cases:
a. a Washington Post/ABC News poll of 2,000
people to determine the president’s approval
rating
b. a poll taken of each of the General Motor
dealerships in Ohio in December 2006 to
determine an estimate of the average number
of 2006 model Chevrolets not yet sold by
GM dealerships in the United States
c. a quality assurance procedure within a
BF Goodrich manufacturing plant that tests
every 1,000th tire produced for cord strength of
the tire
d. a sampling technique in which a random sample
from each of the tax brackets is obtained by the
Internal Revenue Service to audit tax returns
1-42. Your manager has given you an Excel file that
contains the names of the company’s 500 employees and has asked you to sample 50 employees
from the list. You decide to take your sample as
follows. First, you assign a random number to each
employee using Excel’s random number function
Rand(). Because the random number is volatile (it
recalculates itself whenever you modify the file),
you freeze the random numbers using the Copy—
Paste Special—Values feature. You then sort by the
random numbers in ascending order. Finally, you
take the first 50 sorted employees as your sample.
Does this approach constitute a statistical or a
nonstatistical sample?
1-43. According to the U.S. Bureau of Labor Statistics,
the annual percentage increase in U.S. college
tuition and fees in 1995 was 6.0%; in 1999 it was
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4.0%; and in 2004 it was 9.5%. Are these percentages statistics or parameters? Explain.
1-44. According to an article in the Idaho Statesman, a
poll taken the day before elections in Germany
showed Chancellor Gerhard Schroeder behind his
challenger by 6 to 8 percentage points. Is this a statistic or a parameter? Explain.
Computer Applications
1-45. The Craigthorp Company is a statewide food distributor to restaurants, universities, and other establishments that prepare and sell food. The company
has a very large warehouse where the food is stored
until it is pulled from the shelves to be delivered to
the customers. The warehouse has 64 storage racks
numbered 1–64. Each rack is three shelves high,
labeled A,B, and C, and each shelf is divided into
80 sections, numbered 1–80. Products are located
by rack number, shelf letter, and section number.
For example, breakfast cereal is located at 43-A-52
(rack 43, shelf A, section 52).
Each week, employees perform an inventory
for a sample of products. Certain products are
selected and counted. The actual count is compared to the book count (the quantity in the records
that should be in stock). To simplify things, assume
that the company has selected breakfast cereals to
inventory. Also for simplicity sake, suppose the
cereals occupy racks 1 through 5.
a. Assume that you plan to use simple random
sampling to select the sample. Use Excel or
Minitab to determine the sections on each of the
five racks to be sampled.
b. Assume that you wish to use cluster random
sampling to select the sample. Discuss the steps
you would take to carry out the sampling.
c. In this case, why might cluster sampling be preferred over simple random sampling? Discuss.
1-46. United Airlines established a discount airline
named Ted. The managers were interested in determining how flyers using Ted rate the airline
CHAPTER OUTCOME #4
21
service. They plan to question a random sample
of flyers from the November 12 flights between
Denver and Fort Lauderdale. A total of 578 people
were on the flights that day. United has a list of the
travelers together with their mailing addresses.
Each traveler is given an identification number
(here, from 001 to 578). Use Excel or Minitab to
generate a list of 40 flyer identification numbers so
that those identified can be surveyed.
1-47. The U.S. Forest Service has started charging a user
fee to park at selected trailheads and cross-country
ski lots. Some users object to this fee, claiming
they already pay taxes for these areas. The agency
has decided to randomly question selected users at
fee areas in Colorado.
a. Define the population of interest.
b. Assume a sample of 250 is required. Describe
the technique you would use to select a sample
from the population. Which sampling technique
did you suggest?
c. Assume the population of users is 4,000. Use
either Minitab or Excel to generate a list of
users to be selected for the sample.
1-48. The Fairview Title Company has over 4,000 customer files listed alphabetically in its computer
system. The office manager wants to survey a
statistical sample of these customers to determine
how satisfied they were with service provided by
the title company. She plans to use a telephone
survey of 100 customers.
a. Describe how you would attach identification
numbers to the customer files; for example, how
many digits (and which digits) would you use to
indicate the first customer file?
b. Describe how the first random number would be
obtained to begin a simple random sample
method.
c. How many random digits would you need for
each random number you selected?
d. Use Excel or Minitab to generate the list of
customers to be surveyed.
1.4 Data Types and Data Measurement Levels
Chapters 2 and 3 will introduce a variety of techniques for describing data and transforming the data into information. As you will see in those chapters, the statistical techniques
deal with different types of data. The level of measurement may vary greatly from application to application. In general, there are four types of data: quantitative, qualitative, timeseries, and cross-sectional. A discussion of each follows.
Quantitative Data
Measurements whose values are
inherently numerical.
Quantitative and Qualitative Data
In some cases, data values are best expressed in purely numerical, or quantitative terms,
such as in dollars, pounds, inches, or percentages. As an example, a study of college
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Qualitative Data
Data whose measurement scale is
inherently categorical.
Time-series Data
A set of consecutive data values
observed at successive points
in time.
Cross-sectional Data
A set of data values observed
at a fixed point in time.
students at your campus might obtain data on the number of hours each week that students
work at a paying job and the income level of the students’ parents.
In other cases, the observation may signify only the category to which an item
belongs. Categorical data are referred to as qualitative data.
For example, a study might be interested in the class standings—freshman, sophomore, junior, senior, or graduate—of college students. The same study also might ask the
students to judge the quality of their education as very good, good, fair, poor, or very poor.
Note, even if the students are asked to record a number (1 to 5) to indicate the quality level
at which the numbers correspond to a category, the data would still be considered qualitative because the numbers are just codes for the categories.
Time-Series Data and Cross-Sectional Data Data may also be classified as being
either time-series or cross-sectional.
The data collected from the study of college students about their quality ratings would
be cross-sectional because the data from each student relates to a fixed point in time. In
another case, if we sampled 100 stocks from the stock market and determined the closing
stock price on March 15, the data would be considered cross-sectional because all measurements corresponded to one point in time.
On the other hand, Ford Motor Company tracks the sales of its Explorer SUVs on a
monthly basis. Data values observed at intervals over time are referred to as time-series
data. If we determined the closing stock price for a particular stock on a daily basis for a
year, the stock prices would be time-series data.
Data Measurement Levels
Data can also be identified by their level of measurement. This is important because the
higher the data level, the more sophisticated the analysis that can be performed. This will
be clear when you study the material in the remaining chapters of this text.
We shall discuss and give examples of four levels of data measurements: nominal,
ordinal, interval, and ratio. Figure 1.12 illustrates the hierarchy among these data levels,
with nominal data being the lowest level.
Nominal Data Nominal data are the lowest form of data, yet you will encounter this type
of data many times. Assigning codes to categories generates nominal data. For example, a
survey question that asks for marital status provides the following responses:
1. Married
2. Single
3. Divorced
4. Other
FIGURE 1.12
Data Level Hierarchy
Measurements
Rankings
Ordered Categories
Categorical Codes
ID Numbers
Category Names
Ratio/Interval Data
Highest Level
Complete Analysis
Ordinal Data
Higher Level
Mid-Level Analysis
Nominal Data
Lowest Level
Basic Analysis
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23
For each person, a code of 1, 2, 3, or 4 would be recorded. These codes are nominal data.
Note that the values of the code numbers have no specific meaning, because the order of
the categories is arbitrary. We might have shown it this way:
1. Single
2. Divorced
3. Married
4. Other
With nominal data we also have complete control over what codes are used. For example,
we could have used
88. Single
11. Divorced
33. Married
55. Other
All that matters is that you know which code stands for which category. Recognize also
that the codes need not be numeric. We might use
S Single
D Divorced
M Married
O Other
Ordinal Data Ordinal, or rank data are one notch above nominal data on the measure-
ment hierarchy. At this level, the data elements can be rank-ordered on the basis of some
relationship among them, with the assigned values indicating this order. For example, a
typical market research technique is to offer potential customers the chance to use two
unidentified brands of a product. The customers are then asked to indicate which brand
they prefer. The brand eventually offered to the general public depends on how often it was
the preferred test brand. The fact that an ordering of items took place makes this an ordinal
measure.
Bank loan applicants are asked to indicate the category corresponding to their household incomes:
________ Under $20,000
________ $20,000 to $40,000
________ over $40,000
(1)
(2)
(3)
The codes 1, 2, and 3 refer to the particular income categories, with higher codes assigned
to higher incomes.
Ordinal measurement allows decision makers to equate two or more observations or to
rank-order the observations. In contrast, nominal data can be compared only for equality.
You cannot order nominal measurements. Thus, a primary difference between ordinal and
nominal data is that ordinal data contain both an equality () and a greater than () relationship, whereas nominal data contain only an equality () relationship.
Interval Data If the distance between two data items can be measured on some scale and
the data have ordinal properties (, , or ), the data are said to be interval data. The best
example of interval data is the temperature scale. Both the Fahrenheit and Celsius temperature scales have ordinal properties of “” and “.” In addition, the distances between
equally spaced points are preserved. For example, 32°F 30°F, and 80°C 78°C. The
difference between 32°F and 30°F is the same as the difference between 80°F and 78°F,
two degrees in each case. Thus, interval data allow us to precisely measure the difference
between any two values. With ordinal data this is not possible, because all we can say is
that one value is larger than another.
Ratio Data Data that have all the characteristics of interval data but also have a true zero
point (at which zero means “none”) are called ratio data. Ratio measurement is the highest
level of measurement.
Packagers of frozen foods encounter ratio measures when they pack their products by
weight. Weight, whether measured in pounds or grams, is a ratio measurement because it
has a unique zero point—zero meaning no weight. Many other types of data encountered in
business environments involve ratio measurements, for example, distance, money, and time.
The difference between interval and ratio measurements can be confusing because it
involves the definition of a true zero. If you have $5 and your brother has $10, he has twice
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as much money as you. If you convert the dollars to pounds, lire, yen, or marks, your
brother will still have twice as much. If your money is lost or stolen, you have no dollars.
Money has a true zero. Likewise, if you travel 100 miles today and 200 miles tomorrow,
the ratio of distance traveled will be 2/1, even if you convert the distance to kilometers. If
on the third day you rest, you have traveled no miles. Distance has a true zero. Conversely,
if today’s temperature is 35°F (1.67°C) and tomorrow’s is 70°F (21.11°C), is tomorrow
twice as warm as today? The answer is no. One way to see this is to convert the Fahrenheit
temperature to Celsius: The ratio will no longer be 2/1 (12.64/1). Likewise, if the temperature reads 0°F (17.59°C), this does not imply that there is no temperature. It’s simply
colder than 10°F (12.22°C). Also, 0°C (32°F) is not the same temperature as 0°F. Thus,
temperature, measured with either the Fahrenheit or Celsius scale (an interval-level
variable), does not have a true zero.
As was mentioned earlier, a major reason for categorizing data by level and type is
that the methods you can use to analyze the data are partially dependent on the level and
type of data you have available.
E X A M P L E 1 - 1 Categorizing Data
F
or many years U.S. News and World Report has published annual rankings based on
various data collected from more than 1,300 U.S. colleges and universities. Figure 1.13
shows a portion of the data in the file named Colleges. Each column corresponds to a
different factor for which data were collected. Before doing any statistical analyses with
these data, U.S. News and World Report employees need to determine the type and level for
each of the factors. Limiting the effort to only those factors that are shown in Figure 1.13,
this is done using the following steps:
Step 1 Identify each factor in the data set.
The factors (later to be called variables) in the data set shown in
Figure 1.13 are
College State Public (1) Math Verbal ACT # appli. # appli.
# new
% new
Name
Private (2) SAT SAT
rec’d. accepted. stud.
stud.
enrolled from
top 10%
% new # FT # PT
instud.
under- under- state
from
grad
grad
tuition
top 25%
Each of the 14 columns represents a different factor. As shown in
Figure 1.13, data are missing for some colleges and universities.
Step 2 Determine whether the data are time-series or cross-sectional.
Because each row represents a different college or university and the data
are for the same year, the data are cross-sectional. Time-series data are
measured over time—say, over a period of years.
Step 3 Determine which factors are quantitative data and which are
qualitative data.
Qualitative data are codes or numerical values that represent categories. Quantitative data are those that are purely numerical. In this case,
the data for the following factors are qualitative:
College Name
State
Code for Public or Private College or University
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25
FIGURE 1.13
Data for U.S. Colleges and Universities
Data for the following factors are considered quantitative:
MATH SAT
# appl. rec’d.
% new stud. from
top 10%
# PT. undergrad
VERBAL SAT
# appl. accepted
% new stud. from
top 25%
in-state tuition
ACT
# new stud. enrolled
# FT undergrad
Step 4 Determine the level of data measurement for each factor.
The four levels of data are nominal, ordinal, interval, and ratio. This
data set has only nominal-and ratio-level data. The three nominal level
factors are
College Name
State
Code for Public or Private College or University
The others are all ratio-level data.
1-4: Exercises
Skill Development
1-49. What is the difference between qualitative and
quantitative data?
1-50. For each of the following variables, indicate the
level of data measurement:
a. marital status {single, married, divorced, other}
b. home ownership {own, rent, other}
c. college grade point average
d. product rating {1 excellent, 2 good,
3 fair, 4 poor, 5 very poor}
1-51. For each of the following, indicate whether the data
are cross-sectional or time-series:
a. monthly sales
b. unemployment rates by state
c. quarterly unemployment rates
d. employment satisfaction data for a company
1-52. What is the difference between ordinal and
nominal data?
1-53. Consumer Reports, in its rating of cars, indicates
repair history with circles. The circles are either
white, black, or half-and-half. To which level of
data does this correspond? Discuss.
Business Applications
1-54. The manufacturer of a top-selling brand of laser
printers has a support center where customers can
call to get questions answered about their printer.
The manager in charge of the support center has
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recently conducted a study in which she surveyed 2,300 customers. The customers who
called the support center were transferred to a
third party who asked the customer a series of
questions.
a. Indicate whether the data generated from this
study will be considered cross-sectional or timeseries. Explain why.
b. One of the questions asked customers was
approximately how many minutes they had been
on hold waiting to get through to a support person. What level of data measurement is obtained
from this question? Explain.
c. Another question asked the customer to rate
the service on a scale of 1–7, with 1 being
the worst possible service and 7 being the
best possible service. What level of data
measurement is achieved from this question?
Will the data be quantitative or qualitative?
Explain.
1-55. The following information can be found in the
Murphy Oil Corporation 2004 Annual Report to
Shareholders. For each variable, indicate the level
of data measurement.
a. List of Principal Offices (e.g., El Dorado,
New Orleans, Houston, and so on)
b. Income (in millions of dollars) from Continuing
Operations
c. List of Principal Subsidiaries (for example,
Murphy Oil USA, Inc., Murphy Exploration
& Production Company-International, and
so on)
d. Number of New Stations Added in 2004
e. Barrels of Gasoline Sold Per Day in North
America
f. Major Exploration and Production Areas (for
example, Malaysia, Congo, Ecuador, and so on)
g. Capital Expenditures (in millions of dollars) for
example by Function
1-56. You have collected the following information on 15
different real estate investment trusts (REITs).
Identify whether the data are cross-sectional or
time-series.
a. income distribution by region in 2006
b. per share (diluted) funds from operations (FFO)
for the years 2000 to 2006
c. income distribution by region in 2006
d. number of properties owned as of December 31,
2006
e. the overall percentage of leased space for the
119 properties in service as of December 31,
2006
f. dividends per share for the years 2000–2006
1-57. A loan manager for Farmers and Merchants
Bank has the responsibility for approving
automobile loans. In 2004, to assist her in this
matter, she has compiled data on 428 cars
and trucks. These data are in the file called
2004-Automobiles. The variables for which she
has collected data are
Columns Variables
Vehicle Name
Sports Car? (1yes, 0no)
Sport Utility Vehicle? (1yes, 0no)
Wagon? (1yes, 0no)
Minivan? (1yes, 0no)
Pickup? (1yes, 0no)
All-Wheel Drive? (1yes, 0no)
Rear-Wheel Drive? (1yes, 0no)
Suggested Retail Price, what the manufacturer
thinks the vehicle is worth, including adequate
profit for the automaker and the dealer (U.S.
Dollars)
Dealer Cost (or “invoice price”), what the dealership pays the manufacturer (U.S. Dollars)
Engine Size (liters)
Number of Cylinders (1 if rotary engine)
Horsepower
City Miles Per Gallon
Highway Miles Per Gallon
Weight (Pounds)
Wheel Base (inches)
Length (inches)
Width (inches)
Indicate the level of data measurement for each of
the variables in this data file.
1-58. Recently the manager of the call center for a large
Internet bank asked his staff to collect data on a
random sample of the bank’s customers. Data on
the following variables were collected and placed
in a file called Bank Call Center:
Column A
Column B
Column C
Column D
Column E
Column F
Account Number
Caller Sex
Account
Holder Sex
Past Due
Amount
Current
Amount Due
Was this a
Billing Question?
Unique tracking #
1 Male
1 Male
Numerical Value
Numerical Value
2 Female
2 Female
3 Yes
4 No
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27
A small portion of the data is as follows:
Account Number
Caller Gender
Account
Holder Sex
Past Due
Amount
Current
Amount Due
Was this a
Billing Question?
4348291
2
2
40.35
82.85
3
6008516
1
1
0
−129.67
4
17476479
1
2
0
76.38
4
13846306
2
2
0
99.24
4
21393711
1
1
0
37.98
3
c. For each of the six variables, indicate the level
of data measurement.
a. Would you classify these data as time-series or
cross-sectional? Explain.
b. Which of the variables are quantitative and
which are qualitative?
Summary and Conclusions
Business statistics is about converting data into useful information. There are three main components in this process:
descriptive statistics, probability, and inferential statistics.
The tools for descriptive statistics include graphs, charts,
tables, and various numerical measures. Chapters 2 and 3
will introduce the important descriptive tools.
Probability is the way decision makers express their
uncertainty about whether some event will take place. We
use probability distributions as a means of defining
the chances of any outcome occurring based on a set of business conditions. Chapters 4 and 5 introduce the key rules and
concepts you will need to work effectively with probability.
Drawing inferences about a population based on sample
data takes up a good portion of the remainder of the text. We
will introduce you to a variety of inferential tools to help you
learn to think statistically. Figure 1.14 summarizes the differences between populations and samples and the different
types of sampling techniques you may have reason to use.
Businesses have access to more data than ever. Much
of this data they generate internally through normal operations. In other cases, the data they need is found outside the
organization. We have discussed the fact that there are
numerous ways to gather data. Surveys (phone or written)
are effective when gathering data from people. Observation
and direct measurement are appropriate when collecting
data from a process. Figure 1.15 summarizes the most frequently used data collection techniques and the advantages
and disadvantages of each.
The type of data that is collected varies, too. The data
may be quantitative or qualitative, it may be time-series or
FIGURE 1.14
Sampling Techniques
Population
(N items)
Sample
(n items)
Sample
(n items)
Many possible
samples
Sampling Techniques
Nonrandom
Sampling
Convenience Sampling
Judgement Sampling
Ratio Sampling
Random
Sampling
Simple Random Sampling
Stratified Random Sampling
Systematic Random Sampling
Cluster Sampling
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FIGURE 1.15
Data Collection
Method
Data Collection
Techniques
Advantages
Disadvantages
Experiments
Provide controls
Preplanned objectives
Costly
Time-consuming
Requires planning
Telephone Surveys
Timely
Relatively inexpensive
Poor reputation
Limited scope and length
Mail Questionnaires
Written Surveys
Inexpensive
Can expand length
Can use open-ended questions
Low response rate
Requires exceptional clarity
Direct Observation
Personal Interview
Expands analysis opportunities
No respondent bias
Potential observer bias
Costly
cross-sectional, and it may be nominal, ordinal, interval, or
ratio level. The type and level of data that we have is important in determining the type of analysis we can perform.
Please refer to Figure 1.16 for a quick summary of the ways
in which we classify data.
Many of the things you will be doing in this course can be
better done using computer software. The software selected
for this text is Microsoft Excel and Minitab. Although not a
special-purpose statistics software package, Excel contains a
great many tools and techniques for performing descriptive
and inferential statistical analysis. Minitab is a fully functional
statistics package with a spreadsheet look and feel. You will
find that whichever software package is used during this
course, it will be a valuable tool that will free you from tedious
computations, allowing you more time to analyze and interpret
the output to make better business decisions.
FIGURE 1.16
Data Classification
Data Timing
Time-Series
Cross-Sectional
Data Type
Qualitative
Quantitative
Data Levels
Nominal
Ordinal
Interval
Ratio
Key Terms
Arithmetic mean, or average
Business statistics 2
Census 15
Closed-end questions 8
Cluster sampling 20
Convenience sampling 16
Cross-sectional data 22
Demographic questions 8
Experiment 8
Experimental design 8
4
External validity 14
Internal validity 14
Interval data 23
Nonstatistical sampling
techniques 16
Open-end questions 9
Population 15
Qualitative data 22
Quantitative data 21
Rank data 23
Ratio data 23
Sample 15
Simple random sampling 17
Statistical inference tools 5
Statistical sampling techniques 16
Stratified random sampling 18
Structured interview 12
Systematic random sampling 19
Time-series data 22
Unstructured interview 12
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Chapter Exercises
Conceptual Questions
1-59. What level of data is a bar chart most appropriately
used with?
1-60. What level of data is a histogram most appropriately used with?
1-61. Two people see the same movie; one says it was
average and the other says it was exceptional. What
level of data are they using in these ratings? Discuss
how the same movie could receive different reviews.
1-62. Several organizations publish the results of presidential approval polls. Movements in these polls are seen
as an indication of how the general public views presidential performance. Comment on these polls within
the context of what was covered in this chapter.
1-63. The University of Michigan publishes a monthly
measure of consumer confidence. This is taken as a
possible indicator of future economic performance.
Comment on this process within the context of
what was covered in this chapter.
Business Applications
1-64. In a business publication such as The Wall Street
Journal or Business Week, find a graph or chart representing time-series data. Discuss how the data
were gathered and the purpose of the graph or chart.
1-65. In a business publication such as The Wall Street
Journal or Business Week, find a graph or chart representing cross-sectional data. Discuss how the data
were gathered and the purpose of the graph or chart.
1-66. A local television station has asked its viewers to
call in and respond to the question “Do you believe
police officers are using too much force in routine
traffic stops?”
a. Would the results of this phone-in survey be
considered a random sample?
b. What type of bias might be associated with a
data collection system such as this? Discuss
what options might be used to reduce this bias
potential.
1-67. The maker of Creamy Good Ice Cream is concerned about the quality of ice cream being produced by its Illinois plant. The particular trait of
the ice cream of concern is the texture of the ice
cream in each carton.
a. Discuss a plan by which the Creamy Good
managers might determine the percentage
of cartons of ice cream believed to have an
unacceptable texture by potential purchasers
of a particular flavor of their ice cream.
(1) Define the sampling procedure to be used,
(2) the randomization method to be used to
select the sample, and (3) the measurement to
be obtained.
b. Explain why it would or wouldn’t be feasible
(or, perhaps, possible) to take a census to
address this issue.
1-68. A beer manufacturer is considering abandoning can
containers and going exclusively to bottles because
the sales manager believes beer drinkers prefer
drinking beer from bottles. However, the vice president in charge of marketing is not convinced the
sales manager is correct.
a. Indicate the data collection method you
would use.
b. Indicate what procedures you would follow to
apply this technique in this setting.
c. State which level of data measurement applies
to the data you would collect. Justify your
answer.
d. Is the data qualitative or quantitative? Explain.
VIDEO CASE #1
Statistical Data Collection @ McDonald’s
Think of any well-known, successful business in your community. What do you think has been their secret? Competitive products or services? Talented managers with vision? Dedicated
employees with great skills? There’s no question these all play
an important part in their success. But there’s more, lots more.
It’s “data.” That’s right, data.
The data collected by a business in the course of running
its daily operations form the foundation of every decision
made. Those data are analyzed using a variety of statistical
techniques to provide decision makers with a succinct and
clear picture of the company’s activities. The resulting statistical
information then plays a key role in decision making, whether
those decisions are made by an accountant, marketing manager, or operations specialist. To better understand just what
types of business statistics organizations employ, let’s take a
look at one of the world’s most well-respected companies:
McDonald’s.
McDonald’s operates more than 30,000 restaurants in over
118 countries around the world. Total annual revenues recently
surpassed the $20 billion mark. Wade Thoma, vice president of
US Menu Management for McDonalds, helps drive those sales
but couldn’t do it without statistics.
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“When you’re as large as we are, we can’t run the business
on simple gut instinct. We rely heavily on all kinds of statistical data to help us determine whether our products are meeting
customer expectations, when products need to be updated, and
much more,” says Wade. “The cost of making an educated
guess is simply too great a risk.”
McDonald’s Restaurant owner/operators and managers
also know the competitiveness of their individual restaurants
depends on the data they collect, and the statistical techniques
used to analyze the data into meaningful information. Each
restaurant has a sophisticated cash register system that collects
data such as individual customer orders, service times and
methods of payment, to name a few. Periodically, each USbased restaurant undergoes a restaurant operations improvement process, or ROIP, study. A special team of reviewers
monitors restaurant activity over a period of several days, collecting data about everything from front-counter service and
kitchen efficiency, to drive-thru service times. The data are
analyzed by McDonald’s US Consumer and Business Insights
group at McDonald’s headquarters near Chicago to help the
restaurant owner/operator and managers better understand
what they’re doing well, and where they have opportunities
to grow.
Steve Levigne, VP of Consumer and Business Insights
manages the team that supports the company’s decision making efforts. Both qualitative and quantitative data are collected
and analyzed all the way down to the individual store level.
“Depending on the audience, the results may be rolled up to an
aggregate picture of operations,” says Steve. Software packages such as Microsoft Excel, SAS, and SPSS do most of the
number crunching and are useful for preparing the graphical
representations of the information so decision makers can
quickly see the results.
Not all companies have an entire department staffed with
specialists in statistical analysis, however. That’s where you
come in. The more you know about the tools for collecting
and analyzing data, and how to use them, the better decision
maker you’ll be, regardless of your career aspirations. So it
would seem there’s a strong relationship here – knowledge of
statistics and your success.
Discussion Questions:
1. You will recall that McDonald’s vice president of
US Menu Management, Wade Thoma, indicated that
McDonald’s relied heavily on statistical data to determine,
in part, if their products were meeting customer expectations. The narrative indicated that two important sources of
data were the sophisticated register system and the restaurant operations improvement process, ROIP. Describe the
types of data that could be generated by these two methods
and discuss how these data could be used to determine if
their products were meeting customer expectations.
2. One of McDonald’s uses of statistical data is to determine
when products need to be updated. Discuss the kinds of
data McDonald’s would require to make this determination. Also provide how these types of data would be used
to determine when a product needed to be updated.
3. This video case presents the types of data collected and
used by McDonald’s in the course of running its daily
operations. For a moment, imagine that McDonald’s did
not collect this data. Attempt to describe how they might
make a decision concerning, for instance, how much their
annual advertising budget would be.
4. Visit a McDonald’s in your area. While there take note of
the different types of data that could be collected using
observation only. For each variable you identify, determine
the level of data measurement. Select three different variables from your list and outline the specific steps you would
use to collect the data. Discuss how each of the variables
could be used to help McDonald’s manage the restaurant.
References
Berenson, Mark L., and David M. Levine, Basic Business Statistics: Concepts and Applications,
10th ed. (Upper Saddle River, NJ: Prentice Hall, 2006).
Cryer, Jonathan D., and Robert B. Miller, Statitics for Business: Data Analysis and Modeling,
2nd ed. (Belmont, CA: Duxbury Press, 1994).
Fowler, Floyd J., Survey Research Methods, 3rd ed. (Thousand Oaks, CA: Sage
Publications, 2001).
Hildebrand, David, and R. Lyman Ott, Statistical Thinking for Managers, 4th ed. (Belmont, CA:
Duxbury Press, 1998).
John, J. A., D. Whitiker, and D. G. Johnson, Statistical Thinking for Managers. (Boca Raton, FL:
CRC Press, 2001).
Microsoft Excel 2007 (Redmond, WA: Microsoft Corp., 2007).
Minitab for Windows Version 15 (State College, PA: Minitab, 2007).
Pelosi, Marilyn K., and Theresa M. Sandifer, Doing Statistics for Business with Excel, 2nd ed.
(New York: John Wiley & Sons, 2001).
Scheaffer, Richard L., William Mendenhall, and Lyman Ott, Elementary Survey Sampling, 6th ed.
(Brooks/Cole, 2005).
Siegel, Andrew F., Practical Business Statistics, 5th ed. (Burr Ridge, IL: Irwin, 2003).